Linear CMOS transconductance element

ABSTRACT

A simple CMOS linear, tunable, high-frequency transconductance element is described. By using a pair of composite n-channel/p-channel devices, the transconductance circuit achieves its linearity by current differencing without undue matching requirements. The circuit configurations use current differencing to cancel the square-law nonlinearities of the field effect transistors and require approximate matching between transistors of the same type.

This invention was made with Government support under Grant No. ECS 82-15001 awarded by the National Science Foundation. The Government has certain rights in this invention.

BACKGROUND OF THE INVENTION

Integrated analog signal processing systems are inherently encumbered by custom specifications which if implemented in VLSI (Very Large Scale Integration) designs require costly custom design and fabrication. In contrast, VLSI digital systems are easily implemented in less than full custom designs (e.g., semi-custom and gate arrays) due to the highly structured and repetitive use of elementary logic building blocks. The elementary digital logic blocks can be systematically arranged in regular array structures which can be customized to the required application by interconnecting the elementary digital logic blocks to create the required function. If a standard analog building block can be found which lends itself to implementing a wide variety of analog implementations, a standard cell design for analog circuits can be implemented allowing customized VLSI designs by interconnecting a number of elementary linear analog cells in order to achieve a highly systematic design and chip layout with high functional density.

Transconductance elements or voltage-to-current transducers (VCTs) are essential elements of a wide range of analog signal processing circuits. In order for them to be effective, transconductance elements must operate in a linear fashion across a wide input voltage range. Single MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) transistors will act as VCTs but the output current exhibits a non-linear square-law relationship to the input voltage. Multiple transistor linear transconductance elements have been achieved through several approaches by various circuit techniques which compensate for the non-linear term of the basic transistor I-V relationship. These designs have typically required many transistors and consume large amounts of chip surface area.

Bipolar transconductance elements have been used as the basic building blocks in such circuits as operational amplifiers, comparators, and other analog signal processing circuits. MOS technology is, however, more attractive for VLSI semi-custom designs due to its simpler fabrication requirements and higher packing density than bipolar technology. CMOS (Complementary Metal-Oxide-Semiconductor) technology offers the additional advantage of complementary devices and lower power operation.

Prior art linear transconductance elements implemented in CMOS technology have achieved linear operation over a limited voltage range by linearizing a CMOS differential stage using current differencing so that the nonlinear term of the CMOS transistor I-V curve is eliminated. This approach shown in FIG. 1 provides a fairly high gain linear VCT but at a cost of increased chip surface area usage due to the use of many transistors. Several constant current sources are required to provide the current biasing of the circuit which results in a linear VCT implemented in approximately 10 transistors at a minimum.

Simple linear VCTs have been constructed based on using the well-known CMOS inverter by critically matching the gain parameters of the p-MOS and n-MOS transistors in the fabrication of the circuit as shown in FIG. 2. The advantage here is the elimination of the requirement of constant current sources. Unfortunately, power-supply rejection is very poor, the transconductance cannot be tuned, and a very limited linearity has been achieved in practice due to the difficulty of matching the gain constants (μC_(ox) W/L) between the p-MOS and n-MOS transistors. The gain of a p-MOS or n-MOS transistor depends on the physical width-to-length ratio W/L of the gate area, the gate oxide capacitance C_(ox) per unit area, and the effective mobility μ of the charge carriers. Since the effective mobility of electron charge carriers is much greater than the effective mobility of hole charge carriers, the gain constant for an n-MOS transistor is much greater than the gain constant of a p-MOS transistor of the same device dimensions. Therefore the gain of the n-MOS and p-MOS transistors can only be matched by using exact ratios of the width-to-length dimensions of the gates. Since the effective mobility of the charge carriers depends upon doping, bias voltages and temperature, good matching between the p-MOS and n-MOS devices will be difficult to achieve in practice.

To alleviate these difficulties, and to provide for a simple CMOS transconductance element which can be used in regular analog arrays, a linear tunable VCT with as few as four transistors is described. The circuit is constructed by effecting current differencing between two composit transistors, each of which is constructed with a p-channel/n-channel pair of MOSFETs, where the gain of the circuit is tunable by applying fixed reference voltages.

SUMMARY OF THE INVENTION

An improved linear transconductance circuit is described which is comprised of a pair of composite transistors and of a means to achieve current differencing, where each of the composites is constructed using an n-channel/p-channel pair of field effect transistors (FETs) such that the source terminals of the two transistors are connected. The transconductance parameter is tuned by means of a tuning voltage connected to one of the gate terminals of each composite transistor. The tuning voltage is used to bias the assembly of two composite transistors such that it operates linearly.

In one preferred embodiment (Type I), both composite transistors are connected such that the drain terminal of the n-type FET is connected to a heat supply voltage, while the drain terminal of the p-type FET is connected to a low supply voltage. The voltage control signal input is connected to the other unused gate on each of the composite transistors. The difference between the currents in the upper and lower composite transistors forms the linear current output which is controlled by the tuning voltage and is proportional to the signal voltage input.

Accordingly, a tunable voltage to current transducer that exhibits a high degree of linearity is described. This VCT is constructed from two composite transistors and current differencing circuitry. The composite transistors are constructed from a pair of n-MOS/p-MOS FETs with one of the gates acting in each composite transistor as a tuning input for controlling linear operation of the composite.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings of the preferred embodiments of the present invention, wherein like numerals refer to like elements throughout the several views,

FIG. 1 is a prior art transconductance element using current differencing and constant current sources.

FIG. 2 is another prior art transconductance element based on the simple CMOS inverter.

FIG. 3a shows the construction of the composite transistors and their connections.

FIG. 3b is a schematic diagram of a preferred embodiment of the transconductance element. (Type I) The substrate connections are shown using one form of standard notation for MOS technology.

FIG. 3c is another schematic diagram of the preferred embodiment of FIG. 3b using a different notation standard for MOS technology.

FIG. 3d is a schematic diagram of the Type I species of the present invention.

FIG. 3e is a schematic diagram of the Type II species of the present invention.

FIG. 3f is a schematic diagram of the Type III species of the present invention.

FIG. 4 shows the total harmonic distortion (THD) obtained from SPICE simulations of the circuits in FIG. 3b and FIG. 3c by controlling the non-linear behavior of the CMOS devices due to the body effect by width/length ratioing.

FIG. 5 is a plot of the results of SPICE simulation of the circuits in FIGS. 3b and 3c showing the THD as a function of k_(p) /k_(n) for various peak-to-peak input voltages on V_(i).

FIG. 6 shows the simplified small signal model of transistor pair M₁ /M₂ which is identical to the small signal model for transistor pair M₃ /M₄.

FIG. 7 shows the 3 dB- frequency of the circuits in FIGS. 3b and 3c using the small signal model in FIG. 6 plotted for various device dimensions.

FIG. 8 shows a method of biasing the circuit of FIGS. 3b and 3c by use of appropriate n-well bias voltages to eliminate the output DC offset voltage.

FIG. 9 shows a schematic diagram of a method of obtaining V_(G) and -V_(G) for controlling the gain of the circuit described in FIGS. 3b and 3c.

FIG. 10 describes the variation of short circuit output current when V_(G) is varied.

FIG. 11 shows an array of the circuits found in FIGS. 3b and 3c including several tuning circuits of the type found in FIG. 9. This is a schematic example of how a plurality of uncommitted VCT cells could be implemented.

FIGS. 12 through 15 show a few of the possible implementations that can be achieved with the array shown in FIG. 11.

FIG. 16a is a schematic diagram of a Type I single-ended, inverting transconductance circuit.

FIG. 16b is a schematic diagram of a Type I single-ended, non-inverting transconductance circuit.

FIG. 17 is a schematic diagram of a Type II balanced transconductance circuit.

FIG. 18 is a schematic diagram of a Type III fully differential transconductance circuit.

DETAILED DESCRIPTION OF THE TRANSCONDUCTANCE ELEMENT

FIG. 3a shows the two composite devices essential to the construction of the linear tunable high-frequency transconductance element. The transistors are labelled M₁, M₂, M₃, and M₄, where M₁ and M₃ are n-MOSFET devices and M₂ and M₄ are p-MOSFET devices. Transistors M₁ and M₂ form a composite transistor, and transistors M₃ and M₄ form a second composite transistor. One of the gate inputs, for example, V_(G1) or V_(G2), to the first composite transistor is used as the signal input while the other gate input is used for tuning and biasing. The signal source input and the tuning voltage input are interchangeable on the gates. The same is true of the second composite transistor where V_(G3) and V_(G4) are the gate inputs. Either V_(G3) or V_(G4) can for tuning and biasing while the other input is used as the signal input.

In a preferred embodiment described below, V_(G1) and V_(G4) are the tuning voltage inputs while V_(G2) and V_(G3) are used as the signal control voltage input to the VCT. The drain of M₁ is connected to a positive supply voltage source while the drain of M₄ is connected to a negative supply voltage source. The lower drain of the first composite transistor shown in FIG. 3a sources current according to the signal control voltage presented on V_(G1). The drain terminal on transistor M₃ in the second composite transistor likewise sinks a current determined by the amount of signal voltage appearing on V_(G4). The current difference between the first composite transistor and the second composite transistor forms the current output of the device. In FIG. 3a, the current differencing circuitry is not shown and could be formed using current mirrors or other devices, or the outputs could simply be wired together to form a single differencing output. A plurality of VCT circuits based on FIG. 3a can be implemented in a regular array structure of standard cells with each of the aforementioned terminals, i.e., V_(G1), V_(G2), V_(G3), V_(G4), and the current outputs left unconnected. This regular array can be used to implement various analog devices by interconnecting the VCT elements with other elements such as resistors and capacitors to achieve the desired function. The interconnection of the VCT elements with the other components can be accomplished by a simple process of adding one or more layers of metal interconnect over the top of the prefabricated array. The array could include appropriate I/O circuits, analog switches, and other support devices that would be needed to implement a wide variety of analog applications.

The circuits are based on the source-coupled CMOS pairs shown in FIG. 3a. Assuming devices of the same type to be identical and neglecting output conductances and body effect, the currents through the CMOS pairs in FIG. 3a can be expressed as

    I.sub.a =k.sub.eff (V.sub.G1 -V.sub.G2 -V.sub.T).sup.2

    I.sub.b =k.sub.eff (V.sub.G3 -V.sub.G4 -V.sub.T).sup.2

where ##EQU1## and

    V.sub.T =V.sub.Tn -V.sub.Tp

Here, k_(n),p =1/2[μ_(eff) C_(ox) (W/L)]_(n),p, assuming V_(Tn1) =V_(Tn3) =V_(Tn) and V_(Tp2) =V_(Tp4) =V_(Tp), V_(Tp) <0 and V_(Tn) >0 are the threshold voltages μ_(n),p is the effective mobility of the electrons (holes), (W/L) is the width-to-length ratio of the channel, and C_(ox) is the gate-oxide capacitance per unit area. The difference current I_(o) =I_(a) -I_(b) is given by ##EQU2## There are essentially three different combinations of voltages V_(G1), V_(G2), V_(G3), and V_(G4) in FIG. 3a that result in a linear, bias-dependent relationship between the difference current I_(o) and an input voltage V_(i), as shown below.

Type I: Let the voltages at the input terminals be

    V.sub.G1 =-V.sub.G4 =V.sub.B ; V.sub.G2 =V.sub.i +V.sub.S ; V.sub.G3 =V.sub.i -V.sub.s

where V_(i) is the input voltage and V_(B) and V_(S) are bias voltages, as shown in FIG. 3d. Then, the expression for the difference current becomes

    I.sub.o =-4k.sub.eff (V.sub.B -V.sub.S -V.sub.T)V.sub.i =-g.sub.m V.sub.i

where g_(m) is seen to be a linear, large-signal transconductance that can be adjusted linearly via V_(B) and V_(S).

Type II: The second combination of input and bias voltage connections that yields a linear transconductance is illustrated in FIG. 3e:

    V.sub.G1 =V.sub.G3 =V.sub.B ; V.sub.G2 =V.sub.i +V.sub.S ; V.sub.G4 =-V.sub.i +V.sub.S

The resulting equation relating output current I_(o) to input voltage V_(i) is the same as for Type I.

Type III: Finally, applying the voltages

    V.sub.G1 =V.sub.i2 +V.sub.B ; V.sub.G2 =V.sub.i1 -V.sub.S ;

    V.sub.G3 =V.sub.i1 +V.sub.B ; V.sub.G4 =V.sub.i2 -V.sub.S

(FIG. 3f), results in the expression

    I.sub.o =4k.sub.eff (V.sub.S +V.sub.B -V.sub.T)V.sub.id =g.sub.m V.sub.id

where V_(id) -V_(i1) =V_(i2) ; i.e., the output current is proportional to the differential input voltage V_(id).

A preferred embodiment of the simple VCT is shown in FIGS. 3b and 3c (Type I); it uses only four devices, two matched p-MOS and two matched n-MOS transistors that are used as two p-channel/n-channel pairs. All transistors are enhancement mode devices biased in saturation. Assuming approximate matching between the n-MOS devices M₁, M₃, and between the p-MOS devices M₂, M₄, and using the standard square-law model for MOS devices in their saturation region, the currents I_(a) and I_(b) defined in FIG. 3b are easily derived as:

    I.sub.a =k.sub.eff (V.sub.G1 -V.sub.i -V.sub.Tn1 -|V.sub.Tp2 |).sup.2                                         (1a)

    I.sub.b =k.sub.eff (V.sub.i +V.sub.G4 -V.sub.Tn3 -|V.sub.Tp4 |).sup.2                                         (1b)

where ##EQU3## where μ_(eff) is the effective mobility of the charge carriers, C_(ox) the gate oxide capacitance per unit area, W/L the gate width-to-length ratio of the various devices, and V_(Tn1), V_(Tn3) >0, V_(Tp2), V_(Tp4) <0 are the threshold voltages of the corresponding devices. Thus, with equation (1), the output current, I_(o) =I_(a) -I_(b), equals ##EQU4## where the abbreviations ##EQU5## where introduced for the sum and the difference of the threshold voltages, respectively. If the back gate or body effect can be neglected and V_(G1) =V_(G4) =V_(G), ΔV_(T) will be zero so that, by equation (4), the circuit implements an ideal linear VCT, I_(o) =-g_(mT) V_(i), where ##EQU6## is the total transconductance parameter that can be tuned by varying the gate bias voltage V_(G). As explained in the following, V_(G1) and V_(G4) do not necessarily have to be equal for best linearity.

For the devices to stay in their saturation region, as was assumed in the derivation of equation (4), the conditions V_(DS) >V_(GS) =V_(Tn) for n-channel and V_(SD) >V_(SG) -|V_(Tp) | for p-channel devices must be satisfied. This leads to the requirements

    -|V.sub.TP2 |<V.sub.i -V.sub.o <V.sub.Tn3 (7a)

    V.sub.DD V.sub.G -V.sub.Tn1 ; -V.sub.ss <-V.sub.G +|V.sub.Tp4 |                                                (7b)

in addition to

    V.sub.G -V.sub.i >V.sub.Tn1 +|V.sub.Tp2 |(7c)

    V.sub.i -(-V.sub.G)>V.sub.Tn3 +|V.sub.Tp4 |(7d)

to keep all devices on. It is the appropriate choice of V_(G1) and V_(G4) [V_(G) in equation (7)] that causes the VCT to operate linearly. By equation (7a), the limits on linear operation are determined mainly by the threshold voltages of M₂ and M₃, and thus can be extended by increasing V_(Tp2) and V_(Tn3). Without changing the CMOS fabrication process this may be achieved artificially by connecting DC voltage sources V_(zp) and V_(zn) between the input terminal V_(i) and the gates of M₂ and M₃, respectively. Practical methods of implementing such level-shifting circuits are known to those skilled in the art.

Body Effect

The body effect is the effect on channel conductivity due to source-to-substrate biasing. As is known to those skilled in the art, body effect cannot be ignored but must be compensated for in order to create a linear transconductance element. Eliminating the body effect can be done through several methods, such as placing each transistor in its own tub or well; using SOS (silicon-on-sapphire) technology; creating an appropriate substrate bias; or doing accurate width-to-length ratioing of the device dimensions.

The circuit in FIG. 3b implements an ideal linear transconductance g_(mT), given by equation (6), with no DC offset provided that all source-to-substrate voltages, V_(SBi) =V_(Si) -V_(Bi), i=1, . . . , 4, in FIG. 3b are zero. This ideal situation may be achievable with an SOS (silicon-on-sapphire) or a twin-tub CMOS fabrication process. However, placing both the n-MOS and p-MOS transistors in their own well is an additional complication in the CMOS fabrication process that is best avoided if possible for cost and yield considerations.

In this disclosure, a p-type bulk or substrate is assumed with the p-MOS transistors placed in n-wells and the n-channel devices residing directly on the p-substrate. However, those skilled in the art will recognize that an n-type bulk may be used with n-MOS transistors placed in p-wells. Assuming then that V_(SB) is not equal to zero for all devices, the body effect must be taken into consideration.

Including body effect, the threshold voltages for p- and n-channel devices, respectively, can be written as ##EQU7## where γ_(n),p >0 are the body effect coefficients, V_(Tp),no are the threshold voltages for V_(SB) =0, and φ_(n),p are the bulk potentials. It is easy to show that the voltages V_(S1) =V_(S2) =V_(a) and V_(S3) =V_(S4) =V_(b) in FIG. 3b are ##EQU8## where ##EQU9## and k_(n),p was defined in equation (3). Assuming for concreteness in the following an n-well process as discussed above, and setting V_(B1) =V_(B3) =-V_(SS), it can be shown by inserting equation (8) and equation (9) into equation (5), that ##EQU10##

In equation (10a,b), the approximation ##EQU11## has been used and the definitions for p, q, ΔV_(To) and ΣV_(To) are evident. Clearly, from equation (10) and equation (4) body effect results not only in DC offset but also causes ΣV_(T) and ΔV_(T) to depend on V_(i), so that I_(o) is a nonlinear function of V_(i).

For applications requiring extreme linearity, the influence of body effect must be eliminated, a result that can be achieved by W/L ratioing or by appropriate biasing schemes. An easy solution, as revealed by equation (10), consists of setting

    V.sub.B4 =(γ.sub.p /γ.sub.n).sup.2 (V.sub.SS -V.sub.bo +2φ.sub.p)-V.sub.bo -2|φ.sub.n |(11a)

    V.sub.B2 =(γ.sub.p /γ.sub.n).sup.2 (V.sub.SS +V.sub.ao +2φ.sub.p)+V.sub.ao -2|φ.sub.n |, (11b)

which results in both ΣV_(T) and ΔV_(T) to be independent of V_(i).

Further, choosing V_(G1) ≠V_(G4), or specifically by equation (10a) with (11), ##EQU12## reduces ΔV_(T) to zero, thereby eliminating the DC offset.

Thus, the choice of bias voltages given by equations (11) and (12) results in a VCT that is ideally linear and free of offset within the validity of MOS model used and of the approximations made. However, for realistic values of γ_(n) and γ_(p), the required well bias voltages are larger than V_(DD), an inconvenience for practical implementations. A better solution is therefore the last choice mentioned above, that of W/L-ratioing.

Inserting equation (10) into equation (4) gives an expression of the form

    I.sub.o =a.sub.1 +a.sub.2 V.sub.i +a.sub.3 V.sub.i.sup.2   (13)

where a₁ is the DC offset current that after some algebra can be shown to equal ##EQU13## DC offset is eliminated by choosing ΔV_(To) =0, i.e., with V_(G1) =-V_(G4), V_(B2) =V_(a), and (10a) by satisfying the requirement ##EQU14## An offset zeroing method to set the well-voltage V_(B4) to this value automatically is discussed below in the section entitled Offset Control.

With q and p defined in equation (10), the term a₃ in equation (13) can be shown to equal

    a.sub.3 =qk.sub.eff (1-p/4)                                (16)

so that setting q=0 will eliminate the nonlinear term. From (10b) with V_(B2) =V_(a) this requirement results in ##EQU15## where V_(ao), V_(bo) are functions of α with ##EQU16## from (9), and where V_(B4) is chosen according to equation (15). Equation (17) may be solved for the ratio k_(n) /k_(p) such that a₃ =0 and the transconductance is ideally linear. SPICE simulations for several W/L-ratios for the p-channel and n-channel devices are shown in FIG. 4. Curve 41 shows the simulation results for W_(p) /L_(p) =30/10 m, curve 42 indicates the results when W_(p) /L_(p) =90/10 m and curve 43 indicates W_(p) /L_(p) =10/10 m, all for W_(n) /L_(n) =10/10 m, V_(DD) =V_(SS) =V_(G) =5 V. Curve 44 is for the same device dimensions as curve 41 and is included to illustrate the method of extending the linear range by increasing the gate voltage sources (here V_(G) =6 V). Finally, curve 45 shows the improved linearity that can be obtained in the complete absence of body effect as in SOS (silicon-on-sapphire) technology.

Total harmonic distortion (THD) for 1 V, curve 51, and 1.5 V, Curve 52, peak-to-peak input signals is shown in FIG. 5 as a function of k_(p) /k_(n). It is seen that there is a range of W/L-ratios for the n-MOS and p-MOS devices where the VCT has excellent linearity (THD<0.3% for up to 1 V peak-to-peak input signals) and that the exact value of k_(p) /k_(n) for reasonable input signal levels is not critical, with the optimum being approximately k_(p) /k_(n) =1, i.e., W_(p) /W_(n) 3 for L_(n) =L_(p).

Frequency Response

FIG. 6 shows a somewhat simplified small-signal model for the two devices M₁ and M₂ of FIG. 3. In FIG. 6, and in the following equations, the notation

    C.sub.ik =C.sub.gs,k, C.sub.mk =C.sub.gd,k, C.sub.ok =C.sub.ds,k,

    g.sub.ok =.sub.k I.sub.ds,k, G.sub.k =g.sub.mk +g.sub.ok, C.sub.k =C.sub.ik +C.sub.ok,

where k=1,2, has been adopted for the elements. g_(mk) is the appropriate small-signal transconductance parameter, e.g. g_(m2) =k_(p) (V_(SG2) -|V_(Tp2) |), λ_(k) models the effect of channel-length modulation, and k_(n),p was defined in equation (3). Straightforward analysis yields ##EQU17## where terms proportional to s² in the numerator have been neglected because they become dominant only at unreasonably high frequencies. The small-signal model for M₃ -M₄ and the expression for I_(b) are identical to FIG. 6 and equation (18), with all subscripts changed appropriately. Thus, for C_(mk) <<C_(ik), C_(ok) <<C_(ik), g_(ok) <<g_(mk), and if for simplicity it can be assumed that M₁ =M₃ =M_(n), M₂ =M₄ =M_(p), the output current I_(o) =-(I_(a) +I_(b)) is obtained as ##EQU18## If g_(o) /g_(m) <<1 as assumed, the V_(o) -dependent part is negligible, and I_(o) is independent of frequency, ##EQU19## for

    C.sub.in /C.sub.ip =g.sub.mn /g.sub.mp.                    (21)

If all transistors are in saturation, C_(i) and g_(m) for both device types can be expressed as ##EQU20## where d_(ov) is the gate-to-source overlap. Assuming for simplicity d_(ov) <<L, equation (21) with equation (22) results in the condition ##EQU21## Thus, with the total transconductance g_(mT) prescribed and the ratio k_(n) /k_(p) known from equation (17), equation (20) may be solved for ##EQU22## to give the desired value of g_(mT). Further, from equation (17), ##EQU23## gives the best linearity and, from equation (23) with equation (24b), the values ##EQU24## result in the best frequency-response. Finally, W_(n) and L_(n) are chosen as small as practical such that (24a) is satisfied. Note from FIG. 5 that the linearity minimum is quite flat (insensitive to k_(n) /k_(p)). and located at k_(p) /k_(n) ≃1. Thus, with μ_(n) /μ_(p) ≃3, the approximate optimal design is simply, for a suitable choice of W_(n) and L_(n), ##EQU25## FIG. 7 contains the results of SPICE simulations showing the 3 dB-frequency of the short-circuit output current of the VCT in FIG. 3b with W_(p) /W_(n) =1.5 as a function of L_(n) /L_(p). Curve 71 of FIG. 7 shows the simulation results for the channel width W_(p) =15 μm and the source and drain lengths L_(S) =L_(D) =10 μm. Curve 72 indicates the simulation results obtained with W_(p) =15 μm and L_(s) =L_(d) =15 μm. Curve 73 represents W_(p) =30 μm for L_(s) =L_(d) =15 μm. Evidently, the best frequency-response is obtained for the values specified by (25), verifying the analysis presented. As indicated in FIG. 7, without affecting the conclusions reached, the frequency-response depends also on the source and drain areas and perimeters, i.e., for a given width, on the chosen source and drain lengths, L_(S) and L_(D), an effect that is not included in the model of FIG. 6. Thus, as stated above, the devices should be chosen as small as practical if high frequencies are important.

Note that the SPICE results in FIG. 7 indicate 3 dB-frequencies well over 100 MHz for fairly large devices. These results were obtained from a complete SPICE model, including source and drain capacitors and a well-to-substrate capacitance of 0.15 fF/μm² and thus may be considered to be realistic. The device dimensioning described above simply causes a cancellation of the dominant pole-zero pair so that high-order poles and zeros determine the frequency response. Thus, the circuit of FIG. 3a is a very fast extremely linear transconductance element.

Offset Control

It was shown in equation (15) that for V_(B2) =V_(a) an appropriate choice of the n-well voltage V_(B4) will eliminate the output DC offset voltage

    V.sub.o,DC =1/2g.sub.mT R.sub.o ΔV.sub.To

where R_(o) represents the DC load of the VCT and g_(mT) and ΔV_(To) were defined in (6) and (10a), respectively. FIG. 8 shows a simple offset control scheme, with stages C, S and I being a representative of the controlled stages, and a sensing and inverting stage, respectively, all of geometrically identical layout. If the sensor S has a DC offset V_(o),DC for V_(i) =0 and the inverter gain is -A, a voltage V_(B4) =-AV_(o),DC is returned to all the n-well terminals on the chip, resulting in V_(o),DC ≃0 for sufficiently large gain A. V_(c) is adjusted externally or by separate on-chip circuitry to eliminate any offset of stage I. All SPICE simulations of VCTs in this invention disclosure employed this offset control scheme with the resulting V_(o),DC <0.14 mV for A>100.

Transconductance Control

It was pointed out above that the transconductance g_(mT) can be tuned by applying DC control voltages V_(G1) =V_(G4) =V_(G) to the gates of M₁ and M₄. FIG. 9 shows a simple circuit for generating V_(G) and -V_(G) for this purpose. Neglecting channel-length modulation, straightforward analysis yields for V_(DD) =V_(SS) ##EQU26## Note that V_(G) is independent of process parameter variations, but that the control voltage V_(c) is attenuated by the factor 1/n and depends on the power supply voltage. If this causes problems, a more complicated circuit can be used that avoids these drawbacks, as is well known to those skilled in the art. FIG. 10 shows the variation of short circuit output current with V_(DD) =-V_(SS) =12 V, W_(p) /L_(P) =30/30μ and W_(n) /L_(n) =10/30μ when V_(G) is varied from 6 V to 11 V in steps of 1 V.

Detailed Description of the Analog Semi-Custom Array

An analog semi-custom design is the final goal to which this invention is addressed: to develop a sufficiently versatile analog master chip containing elementary linear analog cell (ELAC) arrays that can be customized by one or more metal layers for specific analog signal processing needs. The transconductance element (VCT) described in this invention forms the foundation of this analog semi-custom array. This VCT is implemented in CMOS technology which is compatible with digital circuitry so that if needed, digital gates for control, interfacing or other functions can be integrated on the same IC. The VCT is small and allows for high analog functional density. The VCT arrays can be "programmed" by metal layers and applied control signals to implement a wide range of specifications with the same chip.

The aforementioned VCT is selected as the ELAC forming the foundation of the analog functional building blocks for the analog semi-custom array in the present invention. The VCT-ELAC is used to build a wide variety of circuit components to implement analog functions. By example but not by limitation, the following general purpose continuous-time signal processing circuits can be implemented using the VCT-ELAC: multipliers, operational transconductance amplifiers, gyrators, resistors, buffers, gain stages, low-pass, high-pass, band-pass, all-pass, and band rejection filters along with phase, delay, and magnitude equalizers. All analog components must be electronically variable to allow tuning and automatic compensation against component drifts. The VCT of the present invention is a suitable ELAC because numerous analog building blocks can be implemented by VCTs as shown below.

FIG. 11 shows an example of a group of uncommitted VCT cells. These cells are composed of the aforementioned n-channel/p-channel matched pairs that form the tunable VCT. The cells are fabricated in a regular array structure using CMOS process techniques well known in the semiconductor art. The internal cell connections may be made by metal, polysilicon, or other interconnect techniques known in the art. The cells can be interconnected by forming metal layers over the top of the uncommitted cells in order to implement the semicustom designs. On the right of FIG. 12 are shown two uncommitted tuning cells. These cells can be used to select the tuning voltage of the VCTs. Several of the uncommitted VCT cells may also be assigned to an offset control circuit to provide the appropriate n-well bias voltage to eliminate output DC offset voltage.

VCT-ELAC Array Building Blocks

This section illustrates the realization of several analog circuit components that can be realized by merely interconnecting the VCT-ELACs described above. The following list of components is by no means exhaustive since they are shown by example and not by limitation. The following discussion should serve as an illustration of the potential of this approach.

FIGS. 12-15 depict a "VCT-ELAC array chip" and the fat lines depict the interconnections ("metal layers") necessary to implement a number of analog building blocks. Also included for illustration purposes are some areas for support circuitry, such as for ±V_(G) generation (FIG. 12). Capacitor arrays, switching arrays (transmission gates), and input and output buffers are not shown but are well-known in the semiconductor art and are assumed to be included in this array. Each building block is described briefly below.

A. LINEAR TUNABLE GROUNDED RESISTOR

FIG. 12 (left side) shows a resistor of value R=g_(m) ⁻¹, with g_(m) given in equation (6). The frequency response is as that of g_(m) in FIG. 7.

B. IMPLEMENTING OFFSET CONTROL

FIG. 14 (left side) illustrates DC offset control: under the assumption of n-well technology, V₀ is connected to all lower n-well terminals (not shown). It has been shown above that this feedback control scheme reduces DC offset to a fraction of a millivolt in all ELACs.

C. FOUR QUADRANT MULTIPLIER

FIG. 12 (middle) shows the connections for a four-quadrant multiplier cell realizing I_(o) =4 k_(eff) V_(A) V_(B). Applying I_(o) to the resistor shown on the left of FIG. 12 results in an output voltage, if needed.

D. OPERATIONAL TRANSCONDUCTANCE AMPLIFIER-OTA

OTAs are very useful elements in active filter design. FIG. 13 shows one possibility of many for implementing such a device with VCT-cells. The OTA realizes

    I.sub.o =g.sub.m (V.sup.+ -V.sup.-)

with g_(m) given in equation (6) above. The circuit is designed to exhibit excellent linearity, common-mode rejection, and frequency-range.

E. GYRATOR

High-quality filters need inductors to facilitate response. Inductors in IC form, of course, are simulated by use of gyrators as shown in FIG. 15, Part E1 (grounded inductor, between terminals 1 and ground) and Parts E1 and E2 (floating inductor, between terminals 1 and 2). The performance of FIG. 15 Part E1 is described with

    Z.sub.L.sup.-1 =(jωL+R.sub.L).sup.-1 +jωC.sub.p

where L=C/g_(m) ², R_(L) =g_(o) /g_(m) ², and where C_(p) is the parasitic input capacitor and g_(o) the finite output conductance of the VCT-cell. High-quality inductors, Q>100, for frequencies into the MHz-range can be built.

F. SECOND-ORDER FILTER

FIG. 14 (right side) shows the circuit for a second-order bandpass filter realizing a function of the form

    V.sub.2 /V.sub.1 =as/(s.sup.2 +bs'c)

where b and c are controllable by the Q-control voltage V_(GQ) and the frequency control voltage V_(GF), respectively.

The above examples should be sufficient to illustrate the possibilities of the VCT-ELAC array. Other building blocks are possible. It should be apparent that with the availability of gyrators one can implement floating resistors and transformers, OTAs (or second-order filters) will allow the realization of oscillators, and OTAs can also be used to construct operational amplifiers, comparators, and inverting or non-inverting transconductances.

In a few cases, apparently complicated implementations of building blocks are caused, of course, by the attempt to realize everything by interconnecting identical ELACS. Note too, that all components are constructed using only transistors and, in some cases, capacitors. It is pointed out again that all elements are electronically tunable by applying the necessary bias voltages. FIG. 14 (left side) shows one easy method to realize the required voltages V_(G) and -V_(G), or V_(A) and -V_(A) for the multiplier.

The capacitors needed in most analog signal processing circuits (FIGS. 14 and 15) are, of course, implemented as a capacitor array as is customary in switched-capacitor filters.

G. CURRENT DIFFERENCING TECHNIQUES

Previous discussion has focused upon the simple VCT constructed using a simple wired current differencing technique whereby the drain of M₂ is wired to the drain of M₃ to create the current output I_(o) as shown in FIGS. 3b and 3c. Various alternate current differencing techniques can be used to produce higher output resistance and wider signal swing, within the linear region of operation.

Two linear, tunable, single-ended transconductance elements with high output impedance and wide input and output signal range are shown in FIGS. 16a and 16b. An uppr and a lower current steering configuration consisting of M₅ -I_(BH) and M₆ -I_(BL) are used to form the difference output current. The circuit of FIG. 16a constitutes an inverting transconductance while the circuit in FIG 16b is non-inverting. The input signal rangein FIG. 16a is limited on one side by the condition

    -V.sub.B +V.sub.T <V.sub.i <V.sub.B -V.sub.T

and, in addition for the circuit in FIG. 16a by the condition

    V.sub.II +V.sub.TP2 <V.sub.i <V.sub.I +V.sub.Tn3

to prevent M₃ or M₂ from entering the triode region; V_(I) and V_(II) are the voltages at the nodes I and II respectively. Consequently, the current sources I_(Bh) and I_(Bl) should be of the high swing bias type to achieve an extended signal range while keeping the supply voltages low.

The current differencing technique used in a Type II VCT is shown in FIG. 17. Current steering is used in this case to obtain the two complementary output currents I_(o) and -I_(o) and to achieve an extended band-width. The signal range limitations of this circuit are analogous to those of the circuit in FIGS. 16a and 16b.

A fully differential implementation of current differencing for a Type III VCT is shown in FIG. 18. The two bias voltage sources V_(S) can be realized by two identical level shifters using source follower configurations, as is well-known to those skilled in the art. Circuit operation is otherwise analogous to the circuit of FIG. 17. Here again, the presence of body effect does not cause any DC offset but certainly limits the linear range.

Although specific electrical and physical configurations have been illustrated and described for the preferred embodiment of the CMOS analog standard cell and the linear transconductance element, it will be appreciated by those of ordinary skill in the art that any physical or electrical arrangement which is calculated to achieve the same purpose may be substituted for the specific configurations shown. Thus, although VLSI design is the generally preferred embodiment of the present invention, the devices described herein may be implemented through the use of conventional components in a greater or lesser degree in MSI and SSI designs. Additionally, although p-type and n-type enhancement mode MOSFET transistors have been described and implemented in a CMOS environment for purposes of the preferred embodiment of the present invention, it will be appreciated by those skilled in the art that depletion mode MOS transistors or junction field effect transistors may be substituted therefor. In addition, the field effect transistors may be fabricated in either silicon or gallium arsenide substrate material. Also, MESFET transistors are possible candidates for the implementation of the foregoing invention. Other fabrication techniques will also be apparent to those skilled in the art that lend themselves to the matching of the n-type and p-type transistors as well as suppressing many of the nonlinearities of the transistors and composite transistors by means well biasing, twin tub processing, and silicon-on-sapphire. Also, although CMOS metal gate technology has been described in the present application, silicon gate FET transistors can also be used interchangeably.

While the present invention has been described in connection with the preferred embodiment thereof, it will be understood that many modifications will be readily apparent to those of ordinary skill in the art, and this application is intended to cover any adaptations or variations thereof. Therefore, it is manifestly intended that this invention be limited only by the claims and the equivalents thereof. 

What is claimed is:
 1. A linear voltage to current transducer, comprising:a first composite transistor including a first n-type field effect transistor having gate, drain and source terminals, and a first p-type field effect transistor having gate, drain and source terminals, and having the source terminal of said first n-type transistor connected to the source terminal of said first p-type transistor; a second composite transistor including a second n-type field effect transistor having gate, drain and source terminals, and a second p-type field effect transistor having gate, drain and source terminals, and having the source terminal of said second n-type transistor connected to the source terminal of said second p-type transistor; said second n-type transistor being matched to said first n-type transistor and said second p-type transistor being matched to said first p-type transistor; at least one signal input means connected to at least one of the gate terminals of at least one of said composite transistors for controlling the current through said composite transistors; variable biasing means connected to at least one of the gate terminals of at least one of said composite transistors for biasing all of said n-type and p-type transistors in constant saturation and for adjusting the transconductance; and current differencing means connected between said first composite transistor and said second composite transistor for generating a current output in proportion to the difference between the currents flowing through said first and second composite transistors in linear response to large-signal voltages applied to said at least one signal input means.
 2. The transducer according to claim 1 wherein said current differencing means further includes current steering circuitry connected to said first and second composite transistors with the output of said current steering circuitry forming a difference current output.
 3. The transducer according to claim 1 wherein said variable biasing means comprises voltage level shifting circuitry connected to at least one of the gate terminals of said composite transistors.
 4. The transducer according to claim 1 wherein said variable biasing means comprises tuning voltage means connected directly to at least one of the other gate terminals of at least one of said composite transistors for biasing said composite transistors in constant saturation and for adjusting the transconductance.
 5. The transducer according to claim 1 wherein said first n-type field effect transistor being matched to said seond n-type field effect transistor and said first p-type field effect transistor being matched to said second p-type field effect transistor comprise transistors having substantially identical fabricated geometry.
 6. The transducer according to claim 1 wherein said first n-type field effect transistor being matched to said second n-type field effect transistor and said first p-type field effect transistor being matched to said second p-type field effect transistor comprise parameterically selected transistor pairs such that the parameters of said n-type transistors are nearly identical and the parameters of said p-type transistors are nearly identical.
 7. A linear voltage to current transducer, comprising:a first composite transistor including a first n-type field effect transistor having gate, drain and source terminals, and a first p-type field effect transistor having gate, drain and source terminals, and having the source terminal of said first n-type transistor connected to the source terminal of said first p-type transistor; a second composite transistor including a second n-type field effect transistor having gate, drain and source terminals, and a second p-type field effect transistor having gate, drain and source terminals, and having the source terminal of said second n-type transistor connected to the source terminal of said second p-type transistor; said second n-type transistor being matched to said first n-type transistor and said second p-type transistor being matched to said first p-type transistor; signal input connected to one of the gate terminals of said first composite transistor and further connected to one of the gate terminals of said second composite transistor; first tuning voltage means connected to the other one of said gate terminals of said first composite transistor and second tuning voltage means connected to the other one of said gate terminals of said second composite transistor for receiving tune voltages and for biasing all of said n-type and p-type transistors in constant saturation in response thereto; and current differencing means connected to one of the drain terminals of said first composite transistor and further connected to one of the drain terminals of said second composite transistor for generating a current output in proportion to the difference between the current flowing through said first and said second composite transistors in linear response to a large-signal voltage applied to said signal input.
 8. The transducer according to claim 7 further including first supply voltage connected to the other drain terminal of said first composite transistor and second supply voltage connected to the other drain terminal of said second composite transistor.
 9. The transducer according to claim 7 wherein said current differencing means further includes current steering circuitry connected between said first and said second composite transistors with the output of said current steering circuitry forming a difference current output proportional to said voltage applied to said signal input.
 10. The transducer according to claim 8 wherein one of said supply voltages is placed at ground potential in reference to the other of said supply voltage.
 11. The transducer according to claim 7 wherein a first tune voltage applied to said first tuning voltage means is substantially equal in magnitude and opposite in polarity to a second tune voltage applied to aid second tuning voltage means.
 12. The transducer according to claim 7 further including a first voltage level shifting circuit connected between said signal input and said one of the gate terminals of said first composite transistor and a second voltage shifting circuit connected between said signal input and said one of the gate terminals of said second composite transistor.
 13. A linear voltage to current transducer, comprising:a first composite transistor including a first n-type field effect transistor having gate, drain and source terminals,and a first p-type field effect transistor having gate, drain and source terminals, and having the source terminal of said first n-type transistor connected to the source terminal of said first p-type transistor; a second composite transistor including a second n-type field effect transistor having gate, drain and source terminals, and a second p-type field effect transistor having gate, drain and source terminals and having the source terminal of said second n-type transistor connected to the source terminal of said second p-type transistor; said second n-type transistor being matched to said first n-type transistor and said second p-type transistor being matched to said first p-type transistor; first signal input connected to one of the gate terminals of said first composite transistor; second signal input connected to one of the gate terminals of said second composite transistor; tuning voltage means connected to the other one of said gate terminals of said first composite transistor and further connected to the other one of said gate terminals of said second composite transistor for receiving tune voltages and for biasing said n-type and p-type transistors into constant saturation in response thereto; and current differencing means connected to one of the drain terminals of said first composite transistor, and further connected to one of the drain terminals of said second composite transistor for generating a current output in proportion to the difference between the currents flowing through said first and said second composite transistors in linear response to large-signal voltages applied to said first and second signal inputs.
 14. The transducer according to claim 13 further including a first voltage level shifting circuit connected between said first signal input and one of the gate terminals of said first composite transistor and a second voltage level shifting circuit connected between said second signal input and one of the gate terminals of said second composite transistor.
 15. The transducer according to claim 13 wherein said current differencing means further includes current steering circuitry connected to said first and said second composite transistors with the output of said current steering circuitry forming a difference current output proportional to said voltages applied to said signal inputs.
 16. The transducer according to claim 13 further including first supply voltage source connected to one of the drain terminals of said first composite transistor and second supply voltage source connected to one of the drain terminals of said second composite transistor.
 17. The transducer according to claim 16 wherein one of said supply voltage sources is placed at ground potential in reference to the other of said supply voltage source.
 18. The transducer accordig to claim 13 wherein said current differencing means comprises a direct connection between one of the drain terminals of said first composite transistor and one of the drain terminals of said second composite transistor with said direct connection forming a current difference output proportional to said voltage applied to said signal inputs.
 19. The transducer according to claim 13 wherein said voltages applied to said first signal input are equal in magnitude and opposite in polarity to said voltages applied to said second signal input.
 20. A linear voltage to current transducer, comprising:a first composite transistor including a first n-type field effect transistor having gate, drain and source terminals, and a first p-type field effect transistor having gate, drain and source terminals and having the source terminal of said first n-type transistor connected to the source terminal of said first p-type transistor; a second composite transistor including a second n-type field effect transistor having gate, drain and source terminals, and a seacond p-type field effect transistor having gate, drain and source terminals and having the source terminal of said second n-type transistor connected to the source terminal of said second p-type transistor; said second n-type transistor being matched to said first n-type transistor and being second p-type transistor being matched to said first p-type transistor; first signal input connected to one of the gate terminals of said first composite transistor and further connected to one of the gate terminals of said second composite transistor; second signal input connected to the other one of said gate terminals of said first composite transistor and further connected to the other one of the gate terminals of said second composite transistor; means for biasing all of said n-type and p-type transistors in saturation mode; and current differencing means connected to one of the drain terminals of said first composite transistor and further connected to one of the drain terminals of said second composite transistor for generating a current output in proportion to the difference between currents flowing through said first and second composite transistors in linear response and proportion to large-signal voltages applied to said signal inputs.
 21. The transducer according to claim 20 further including a first voltage level shifting circuit connected between said first signal input and one of said gate terminals of said first composite transistor, a second voltage level shifting circuit connected between said first signal input and one of said gate terminals of said second composite transistor, third voltage level shifting circuit connected between said second signal input and the other one of said gate terminals of said first composite transistor, and fourth voltage level shifting circuit connected between said second signal input and the other one of said gate inputs of said second composite transistor.
 22. The transducer according to claim 20 wherein said current differencing means further includes current steering circuitry connected to said first and second composite transistors with the output of said current steering circuitry forming a difference current output.
 23. The transducer according to claim 20 wherein said current differencing means comprises a direct connection between one of the drain terminals of said first composite transistor and one of the drain terminals of said second composite transistor with said direct connection forming a difference current output.
 24. The transducer according to claim 20 further including a first voltage supply source connected to one of the drain terminals of said first composite transistor, and second voltage supply source connected to one of the drain terminals of said second composite transistor.
 25. The transducer according to claim 24 wherein one of said voltage supply sources is placed at ground potential in reference to the other. 